Multi-objective compliance control of redundant manipulators: Hierarchy, control, and stability

Robots with a large number of actuated degrees of freedom are usually redundant w.r.t. a given task. That kinematic redundancy can be utilized to execute additional tasks simultaneously, e. g. via null space projection techniques. We introduce a new representation of hierarchical robot dynamics which are based on a set of particular null space velocities. Dynamic consistency is preserved, and strict compliance with the order of priority is ensured at all times due to a power-conserving cancellation of coupling terms by active control. No external force measurements have to be performed. We show asymptotic stability of the generic closed-loop system with an arbitrary number of hierarchy levels. Several simulations confirm our results.